Washington
— Officially, it's billed as a personal visit. But now that he has attended his son's graduation from Brown University Saturday, Jordan's King Hussein will take care of some business as well.

In a round of meetings this week with American officials, including President Reagan Wednesday, King Hussein is expected to press for more active United States involvement in the Mideast peace process. In addition, Hussein will take his case to Congress for more US aid to Jordan.

Jordan has become the central player in efforts to form an alliance of moderate Arab states and the Palestine Liberation Organization (PLO) to negotiate the return of territories occupied by Israel since the 1967 Arab-Israeli war: the West Bank, the Gaza Strip, and the Golan Heights.

The peace process received a substantial boost last February when PLO chief Yasser Arafat agreed to help form a joint Jordanian-Palestinian team for possible peace talks with Israel, which would be based on the ``land for peace'' formula embodied in UN Resolution 242.

But the move, which Hussein has described as the ``last chance'' for peace in the Middle East, quickly bogged down over the question of who should speak for the Palestinians.

Palestinians insist that the PLO is their only legitimate bargaining representative. Israel has refused to talk with any Palestinians unless they agree to recognize Israel, accept UN Resolutions 242 and 338, and renounce the use of terrorism. Israel recently rejected a compromise proposal calling for the participation of non-PLO members of the Palestine National Council, the Palestinians' parliament in exile.

Experts say the main problem now is that Hussein is not ready to move without the PLO's approval. In turn, the Reagan administration is not ready to move without Israel's approval. Reagan administration officials are reluctant to push the Israeli government to the point where its ruling coalition loses popular support.

When Hussein meets with Mr. Reagan tomorrow, the focus will be on the process of getting to negotiations.

``The two parties approach each other with quite different agendas,'' says William Quandt of the Brookings Institution. ``Hussein feels the need for some positive sign from the Americans to pull Arafat over the last hurdle to get a formula for the delegation.''

For example, he says, Hussein will be looking for more US flexibility on the question of Palestinian representation or perhaps ``some verbal American position that inches toward the Palestinian demand for `self-determination' in the West Bank.'' But Reagan will probably tell Hussein that ``it's really up to you'' to find an acceptable delegation, Mr. Quandt says.

``Generally, the prospects for peace are better than they've been for a long time,'' says one State Department official. ``But getting talks started is a slow, grinding process -- like working your way through a fog, trying to find the right path.''

Regardless of whether such a path can be found, Hussein's efforts to move the peace process forward may strengthen his chances for securing more US military aid. So far, the Reagan administration has not specifically asked Congress to send arms to Jordan, pending the completion of a study commissioned in January by national-security adviser Robert C. McFarlane to review all US arms sales to the Middle East.

It is expected that when the request does come, it will meet with spirited congressional opposition. Last year, congressional pressure forced the administration to abandon efforts to sell Stinger shoulder-fired anti-aircraft missiles to Jordan.

This year, in a move with possible majority support, some House members are seeking to peg the future sale of new or advanced arms to Jordan's willingess to recognize and negotiate with Israel.

``I commend [Hussein] for trying to take steps toward peace,'' says Rep. Larry Smith (D) of Florida, principal sponsor of the House measure. ``But we have to say, `Until you give us something we can utilize in the peace process, you can't expect us to give you everything you want.' ''

Administration officials say selling new arms to Jordan is consistent with the US policy of shoring up moderate regimes in the region. ``It's a complement to the peace process,'' says the State Department spokesman. ``Countries have to be confident of their security to take the risk for peace. Jordan's taken the first step. Now it's our turn.''